# problem with line integral

• Jan 6th 2010, 03:04 AM
vonflex1
problem with line integral
hi, this is my problem:

i need to find the mass of the curve (which is shown in parametric form):

$x = e^tcos(t), y = e^tsin(t), z = e^t$

from $t=0$ to $t=a$

and the mass density of the line is reversely proportional to

$x^2 + y^2 + z^2$

and also $\rho (1,0,1) = 1$

i am having trouble with it - is reversely proportional means

$\frac{1}{x^2+y^2+z^2}$,

and if so what am is supposed to do with $\rho$?
• Jan 6th 2010, 04:13 AM
HallsofIvy
Quote:

Originally Posted by vonflex1
hi, this is my problem:

i need to find the mass of the curve (which is shown in parametric form):

$x = e^tcos(t), y = e^tsin(t), z = e^t$

from $t=0$ to $t=a$

and the mass density of the line is reversely proportional to

$x^2 + y^2 + z^2$

and also $\rho (1,0,1) = 1$

i am having trouble with it - is reversely proportional means

$\frac{1}{x^2+y^2+z^2}$,

and if so what am is supposed to do with $\rho$?

Well, I've never seen "reversely" proportional. In fact I don't believe that "reversely" is a word in the English language! I suspect this is a mis-translation of "inversely proportional" which means just what you say: a multiple of $\frac{1}{x^2+ y^2+ z^2}$.

" $\rho(x,y,z)$" is the density function. While it is not a standard notation, since it is the only function given, I am sure that must be the case- and I suspect that previous examples in your text have used " $\rho$" to mean the density function. You are told two things:
1) $\rho= \frac{k}{x^2+ y^2+ z^2}$ and
2) $\rho(1, 0, 1)= \frac{k}{1^2+ 0^2+ 1^2}= 1$
You can use that to find k and so find the full density function.

Of course, the mass is just the density function integrated over the curve.
• Jan 6th 2010, 04:32 AM
vonflex1
thanks,

i did mean inversely, it's just first time i have to translate that expression
to english.

in any case, my problem was that i didn't know about that k...